In recent years several multi-dimensional trellis codes have been discovered which provide a better performance against Gaussian noise than two-dimensional trellis codes of similar complexity. These trellis codes have minimum-distance error patterns which are only one or two symbol intervals long. (In what follows, unless indicated otherwise, symbols are assumed to be two-dimensional.) When noise has a Gaussian distribution, the performance of the trellis code is determined by a minimum-distance of the trellis code, and the lengths of the minimum-distance error patterns do not directly affect the performance.
However, when the noise probability density exhibits long tails (signifying a high probability for large noise peaks), the performance can be noticably degraded when minimum-distance error patterns are very short. For such noise, the advantage of multi-dimensional trellis codes may be lost. In practice, large noise peaks may be caused by impulsive noise or by signal-dependent impairments such as non-linear distortion or pulse code modulation (PCM) noise found in the analog public switched telephone network.
In multi-dimensional trellis codes, short minimum-distance error patterns are created by parallel transitions in the trellis diagram. A method which is known in the art as multi-level coding can eliminate these short minimum-distance error patterns. In multi-level coding, extra parity bits are added in the transmitter so that the receiver can detect and correct parallel transition errors. A special form of multi-level coding involves single parity-check (SPC) block codes. With multi-level coding, a synchronized receiver can detect minimum-distance parallel transition errors, as long as there is only one type of error per SPC frame.
In data transmission systems, it is often necessary to maintain symbol frame synchronization between transmitting and receiving modems. In what follows, this will be called primary frame synchronization. Primary frame synchronization is necessary, for example, in data transmission systems that employ multiplexers. A transmission system in which a fractional number of bits must be transmitted per symbol (on the average) is another example of a system that requires symbol frame synchronization. In a system utilizing multi-level trellis coding with SPC's, the primary frame size may be different from the length of the SPC code.
In practice, primary frame synchronization is established prior to data transmission using a preamble or training sequence. However, during data transmission primary frame synchronization may be lost due to a sudden change in the channel delay between the transmitter and receiver. It is important that during data reception such loss of primary frame synchronization be quickly detected. In a commonly used technique, known frame synchronization bits (frame sync bits) are added at primary frame boundaries at the transmitter using time-division multiplexing. In the receiver, a frame synchronization loss detector checks whether the bits received in the designated primary frame boundaries correspond to the frame sync bits. When this check fails more than a predetermined number of times over a predetermined period of time, a loss of frame synchronization is declared. A disadvantage of this technique is that a portion of the channel capacity must be allocated for frame synchronization to transmit the frame sync bit.
Thus, there is a need for quickly detecting and correcting a loss of frame synchronization in a communication system that uses multi-level trellis coding.